Dimensional crossover of Bose-Einstein condensation of atomic gases in anisotropic harmonic traps

We investigate the dimensional crossover of Bose-Einstein condensation of atomic gases trapped in anisotropic harmonic potentials. The crossover from three dimension to lower dimensions is studied by calculating some thermodynamic quantities, such as critical temperature, heat capacity, entropy and atom number fluctuations in Bose-Einstein condensate. The smooth transition behavior indicates that a decimal dimension may be employed to describe the corresponding intervenient states. We compare the theoretical curves with recent experimental results on the fluctuations of the condensate atom numbers, revealing how the geometry and size of the condensates affect the thermodynamic characteristics.